Orthogonal Frequency Division Multiplexing (OFDM) systems transmit multiple subcarriers at the same time using a multitude of frequencies. An example OFDM signal is shown in FIG. 1, including data subcarriers and pilot subcarriers. FIG. 1 shows a frequency axis and a time axis, and the subcarriers (both pilot and data subcarriers) with the same time index together make up a symbol.
When an OFDM signal is transmitted and then received by a receiver, the received signal is somewhat different from the transmitted signal, as shown in Equation 1, where y(t,k) is the received subcarrier symbol, x(t,k) is the transmitted subcarrier symbol, H(t,k) is the channel frequency response of the subcarrier symbol, and n(t,k) is noise. The channel frequency response is given by Equation 2. Thus, discounting issues of noise, the transmitted signal can be known if the channel frequency response is also known. OFDM receivers typically calculate channel frequency response (also called “channel estimation”) in order to get the transmitted subcarriers before demodulation is performed.y(t,k)=x(t,k)×H(t,k)+n(t,k)  Equation 1H(t,f)=∫h(t,τ)e−j2πfτdτ  Equation 2
OFDM signals typically have subcarriers with known properties to assist in calculating channel frequency response. One example is training symbols, as used in bursty transmissions, such as in IEEE 802.11a/g. Another approach is to use pilot subcarriers distributed throughout the signal, as in WiMax, Digital Video Broadcasting (DVB) and others. For instance, FIG. 1 includes pilot subcarriers. Pilots are also referred to as known tones because x(t,k) is known for a given pilot, and the known x(t,k) can be used to calculate the channel frequency response for the given pilot, as in Equation 3.{dot over (H)}(t,k)=y(t,k)/x(t,k)  Equation 3
DVB uses two kinds of pilots. First, there are scatter pilots, where one pilot tone is used every twelve tones in the frequency domain. The positions are cyclically shifted by three subcarriers every adjacent OFDM symbol. The other kinds of pilots are continual pilots, where certain tones (with indices of 0, 48, 54, 87, . . . , 1704, . . . , 6816) of every OFDM symbol are known.
In DVB, scatter pilots are used to calculate the channel frequency response for the data subcarriers in the signal. The channel frequency response at scatter pilot positions are estimated by a least square (LS) method, i.e., using Equation 3. The channel frequency response of data subcarriers are further estimated from these obtained LS estimations of the pilots. There are currently many techniques in use to estimate the channel frequency response of data subcarriers from that of pilots.
One technique to estimate the channel frequency response of a data subcarrier from a pilot subcarrier is piecewise linear interpolation and higher order polynomial fitting. Such technique ignores the noise effect, and does not need channel statistic information. It provides low to moderate complexity and performance.
Another technique is the transform domain method. The transform domain method needs channel statistic information (Signal to Noise Ratio, time and frequency domain correlation) and uses Fast Fourier Transform (FFT) and Inverse FFT/IFFT calculations. The transform domain method has a moderate to high complexity and performance.
Yet another technique is the Minimum Mean Square Error (MMSE) method, which typically uses channel statistic information and has moderate complexity and high performance. Conventional MMSE methods are one-dimensional (1-D), either in the time or frequency domain. A 1-D MMSE method looks only to pilots with the same frequency or time index as the data subcarrier which is being estimated. Some MMSE methods use both a 1-D time domain estimation and a 1-D frequency domain estimation (also called a sequential 1-D method) but are not truly two-dimensional (2-D) because pilots with different frequency and time indices from the data subcarrier being estimated are not able to be used in the estimation. However, true 2-D MMSE estimation has been described to some extent in the prior art. Currently available MMSE methods fail to strike an adequate balance between efficiency and accuracy by performing needless recalculating and/or performing estimation using more pilots than is necessary.